A search weighted positioning method based on TDoA

Abstract

The present invention discloses a search weighted positioning method based on TDoA. When the number of base stations is equal to 3, an analytical solution is directly obtained by establishing an equation, and the analytical solution is the final target estimated position; when the number of base stations is greater than 3, the number of combinations of three base stations is calculated, and the analytical solution of the target position is solved based on TDoA for each combination; based on the analytical solution of the target position, a rectangular search area is constructed; then a candidate position is selected, and the weight of the corresponding candidate position is calculated for all candidate positions; the weight is substituted into the constructed objective function, and the objective function value corresponding to all candidate positions is calculated; the minimum value is found from the objective function values ​​corresponding to all candidate positions calculated, and the candidate position corresponding to the minimum value is the final target estimated position. This method not only considers the influence of measurement error, but also considers the influence of geometric conditions on position estimation, makes full use of redundant information, and improves the accuracy of position estimation.

Description

Technical Field

[0001] The present invention relates to the field of positioning and navigation technology, and in particular to a search weighted positioning method based on TDoA. Background Art

[0002] Time Difference of Arrival (TDoA) is one of the widely used measurements in the field of positioning. It refers to the time difference between the target receiving the signals transmitted by different base stations, or the time difference between different base stations receiving the target's transmitted signals. The advantage of a positioning system based on TDoA is that it does not require time synchronization between the base station and the target, thereby reducing the cost and complexity of system design.

[0003] TDoA-based positioning algorithms have been widely studied and are mainly divided into three categories: nonlinear optimization methods, linear methods, and geometric methods. Nonlinear optimization methods include Gauss-Newton method, gradient descent method, etc. The disadvantage is that the performance is related to the selected initial value and may fall into the local optimal solution during the iterative solution process; linear methods mainly include two-step weighted least squares algorithm, constrained weighted least squares algorithm and separated constrained weighted least squares algorithm, etc. The two-step weighted least squares algorithm and constrained weighted least squares algorithm can reach the Cramer-Rao lower bound when the noise is small, but the positioning effect is very poor under special geometric conditions. The separated constrained weighted least squares algorithm can avoid the ill-conditioning of the system matrix by separating the position coordinates and auxiliary variables on both sides of the equation. In summary, since the weighted least squares method ignores the higher-order terms of noise, it can approach the Cramer-Rao derive estimation performance under smaller measurement noise, but as the measurement noise increases, the estimated error will deviate from the Cramer-Rao derive, especially when the base stations are distributed in a uniform circular array and the target is close to the base station, the noise resistance is poor; the geometric method mainly includes the circle shrinkage method, which has low computational complexity, but cannot use redundant measurement information to improve positioning accuracy. Summary of the invention

[0004] The purpose of the present invention is to provide a search weighted positioning method based on TDoA, which not only takes into account the influence of measurement errors, but also takes into account the influence of geometric conditions on position estimation, makes full use of redundant information, and improves the accuracy of position estimation.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A search weighted positioning method based on TDoA, the method comprising:

[0007] Step 1: When the number of base stations is equal to 3, an analytical solution is directly obtained by establishing an equation, and the analytical solution is the final target estimated position;

[0008] Step 2: When the number of base stations is greater than 3, calculate the number of combinations of three base stations, and solve the analytical solution of the target location based on TDoA for each combination;

[0009] Step 3: Based on the analytical solution of the target position obtained in step 2, a rectangular search area is constructed;

[0010] Step 4: Then select candidate positions in the constructed rectangular search area, and calculate the weights of the corresponding candidate positions for all candidate positions;

[0011] Step 5: Substitute the weight calculated in step 4 into the constructed objective function to calculate the objective function values ​​corresponding to all candidate positions; wherein the objective function is the weighted sum of squares of the deviations between the measured values ​​and the true values;

[0012] Step 6: Find the minimum value from the objective function values ​​corresponding to all the candidate positions calculated. The candidate position corresponding to the minimum value is the final target estimated position.

[0013] It can be seen from the technical solution provided by the present invention that the above method not only takes into account the influence of measurement errors, but also takes into account the influence of geometric conditions on position estimation, makes full use of redundant information, improves the accuracy of position estimation, can reflect whether there are anomalies in many measurements, and has the ability to shield abnormal measurements. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0015] Figure 1 A schematic diagram of a TDoA-based search weighted positioning method flow chart provided in an embodiment of the present invention;

[0016] Figure 2 Schematic diagram of a rectangular search area in an embodiment of the present invention;

[0017] Figure 3 Schematic diagram of the shortest distance between a candidate position and a single hyperbola after the coordinate system is transformed in an embodiment of the present invention;

[0018] Figure 4 A schematic diagram of a search method for solving r in general in an embodiment of the present invention;

[0019] Figure 5 Schematic diagram of solving r under special circumstances of an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments, which does not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0021] like Figure 1 FIG. 1 is a flow chart of a TDoA-based search weighted positioning method provided by an embodiment of the present invention, wherein the method comprises:

[0022] Step 1: When the number of base stations is equal to 3, an analytical solution is directly obtained by establishing an equation, and the analytical solution is the final target estimated position;

[0023] In this step, two-dimensional is taken as an example, and the same is applicable to three-dimensional cases. The specific process is as follows:

[0024] Assume that the coordinates of the i-th base station are S i (x i ,y i ,h i ), where h i is the vertical height difference between base station i and the target, i = 1, 2, ..., N, N is the total number of base stations, and the actual position of the target at the kth moment is P k (x k ,y k ), and its estimate is

[0025] To achieve TDoA-based positioning, at least three base stations are required, that is, N ≥ 3. The known TDoA measurement can be converted into a distance-related measurement, as shown in formula (1):

[0026]

[0027] Where c is the speed of sound in m / s. Base station 1 is used as the reference point, and the target and base station S i The difference between the distance between the base station and the reference base station;

[0028] When N = 3, use the measurement Instead of real RDOA i1，k , the solution obtained Yes P k The specific solution process is as follows:

[0029]

[0030] Subtract ① from ② and ③ in formula (2) to get:

[0031]

[0032] in is the distance between the target and base station 1; x 12 =x1-x2,y 12 =y1-y2,x 13 =x1-x3,y 13 =y1-y3,

[0033] The solution of formula (3) can be divided into two cases:

[0034] The three base stations are not on the same straight line, that is, x 12 y 13 ≠x 13 y 12 ; The three base stations are on the same straight line, that is, x 12 y 13 =x 13 y 12 ;In both cases, the three base stations are at different locations;

[0035] When x 12 y 13 ≠x 13 y 12 When , we can get from formula (3) and The relationship is shown in formula (4):

[0036]

[0037] in,

[0038]

[0039] Substituting equation (4) into equation (2) yields a The quadratic equation of one variable is as follows:

[0040]

[0041] in,

[0042]

[0043] Obviously, equation (6) has two solutions, but only one of them can be selected as Solution, let Δ = b 2 -4ac, select The guidelines are as follows:

[0044] ① If Δ ≥ 0, equation (6) has two real roots, namely (-b + √Δ) / (2a) and (-b - √Δ) / (2a). If both roots are positive, the smaller one is chosen as Otherwise, choose the larger one;

[0045] ② If Δ<0, equation (6) has two complex roots, then take its real part as The solution is

[0046] Bundle Substituting into equation (4) we can get the estimated position of the target

[0047] When x 12 y 13 =x 13 y 12 When , equation (4) is not valid because the denominators in equation (5) are all zero. Therefore, equation (3) needs to be solved by the following method, which can be divided into three cases:

[0048] 1) If x 12 =0, there must be y 12 ≠, otherwise base station 1 and base station 2 are at the same location, so x 13 =0 and y 13 ≠0, multiply both sides of equation (3) by y 13 , and multiply both sides of equation ② by y 12 ,So It can be solved by formula (8):

[0049]

[0050] 2) If y 12 =0, same as situation ①, there must be x 12 ≠0, then x 13 ≠0 and y 13 =0, at this time Solve through formula (9):

[0051]

[0052] 3) If x 12 ≠0 and y 12 ≠0, then It can be solved by equation (8) or (9);

[0053] In seeking Then, substitute it into equations ① and ② in equation (2) to obtain the estimated position of the target.

[0054] In a specific implementation, when N=3, the target position solution method can not only solve the situation where the three base stations are not on a straight line, but also solve the situation where the three base stations are on the same straight line.

[0055] Step 2: When the number of base stations is greater than 3, calculate the number of combinations of three base stations, and solve the analytical solution of the target location based on TDoA for each combination;

[0056] In this step, when the number of base stations is greater than 3, that is, N>3, for N base stations, there are M 3-base station combinations, and the value of M is determined by the following formula, where 'C' represents a combination operator and '! ' represents a factorial operator:

[0057]

[0058] For M combinations of three base stations, each base station combination uses the solution method when N=3 in step 1 to find an analytical solution for the target estimated position, a total of M, forming a set S.

[0059] Step 3: Based on the analytical solution of the target position obtained in step 2, a rectangular search area is constructed;

[0060] In this step, if Figure 2 The figure is a schematic diagram of a rectangular search area in an embodiment of the present invention. The process of constructing the rectangular search area is specifically as follows:

[0061] Using the minimum value of the horizontal coordinate of all three base station combination solutions and maximum value And the minimum value of the vertical axis and maximum value Construct the vertex coordinates of the rectangular search area:

[0062] and

[0063] Step 4: Then select candidate positions in the constructed rectangular search area, and calculate the weights of the corresponding candidate positions for all candidate positions;

[0064] In this step, the process of selecting candidate positions in the constructed rectangular search area is as follows:

[0065] like Figure 2 As shown, m horizontal lines and n vertical lines are used to equally divide the rectangular search area, and the intersections of the horizontal lines and the vertical lines, the intersections of the horizontal lines and the rectangular sides, the intersections of the vertical lines and the rectangular sides, and the vertices of the rectangle constitute all candidate positions, totaling (m+2)·(n+2). It is worth noting that the values ​​of m and n are set as needed, and can be equal or selected according to the ratio of the length of the rectangle side.

[0066] In the specific implementation, the weight calculation process corresponding to the candidate position is:

[0067] First, the noise is measured at the distance difference between the candidate location and the two base stations to obtain

[0068] After the rotation and translation of the coordinate system, for the general case, the coordinates of the two base stations and Constructing a single standard hyperbola, and solving the shortest distance r from the candidate position to the single standard hyperbola;

[0069] For special cases, the coordinates of the two base stations and Construct a straight line or ray, and calculate the shortest distance r from the candidate position to the straight line or ray;

[0070] The weight α i，j Calculate according to the following formula:

[0071] α i，j =1 / r 2 .

[0072] For example, the weight α i，j The specific calculation process is:

[0073] Choose two different base stations S i and S j , whose coordinates are S i (x i ,y i ), S j (x j ,y j );

[0074] Select a candidate position with coordinates T(x t ,y t ), then the unknown position of the target and the base station S i and S j The distance difference RDOA i，j The value of can be calculated by formula (12):

[0075]

[0076] Set the current measurement noise to Δd i，j ,make

[0077] Assume there is a position point Q that satisfies where ||QS i || represents point Q and base station S i distance;

[0078] In general, when When , point Q is on a hyperbola;

[0079] In special cases, when When Q is on a straight line, When , point Q is on the ray;

[0080] ① For general situations, that is

[0081] In order to calculate the weights conveniently, the coordinate system needs to be transformed first, that is, rotation and translation operations are performed so that after the coordinate system transformation, the base station S i and S j They are on the x-axis, and their centers are at the origin. The method of rotating and translating the coordinate system is shown in formula (13):

[0082]

[0083] in:

[0084]

[0085]

[0086] After the coordinate system is transformed, A single standard hyperbola is constructed for the distance difference. After the rotation and translation of the coordinate system, the equation of the constructed single standard hyperbola is as follows:

[0087]

[0088] in:

[0089] b 2 =c 2 -a 2

[0090] like Then take the left branch of a single standard hyperbola (14); if Then take the right branch of a single standard hyperbola (14);

[0091] Assume that the candidate position T(x t ,y t ) after rotation and translation according to formula (13) is T′(x′ t , y′ t ), with T′(x′ t , y′ t) as the center, when the circle is tangent to a single branch of the single standard hyperbola (14), the radius r is the shortest distance from the position of the point to be determined to the hyperbola; the larger the r, the smaller the contribution of the corresponding measurement to the accuracy of the final position estimation under the current measurement error and geometric conditions, and the smaller the corresponding weight should be; conversely, the smaller the r, the greater the contribution of the corresponding measurement to the accuracy of the final position estimation, and the larger the weight.

[0092] Assuming the coordinates of the tangent point are P′0(x′0, y′0), then r=||T′P′0||, such as Figure 3 FIG. 1 is a schematic diagram of the shortest distance between a candidate position and a single hyperbola after the coordinate system is transformed in an embodiment of the present invention. However, P′0(x′0, y′0) is not easy to solve directly. Therefore, the present invention proposes a numerical search solution method, that is, searching for a point P′0(x′0, y′0) on a single standard hyperbola that satisfies [(x′ t -x′0) 2 +(y′ t -y′0) 2 ]minimum;

[0093] To speed up the numerical solution, Figure 4 The figure shows a schematic diagram of the search method for solving r in general under the embodiment of the present invention. The present invention limits the search range to between two points A and B on a single standard hyperbola, where point A (x′ A , y′ A ) is a point through T′(x′ t , y′ t ), and the intersection of the straight line perpendicular to the asymptote and the single standard hyperbola; point B(x′ B , y′ B ) is the straight line y′=y′ t Intersection point with a single standard hyperbola;

[0094] The following takes the right branch of the standard hyperbola as an example to introduce the process of determining the coordinates of points A and B:

[0095] When y′ t ≥0, through point T′(x′ t , y′ t ) and the equation of the line perpendicular to the asymptote is:

[0096]

[0097] When y′ t <0, passing through point T′(x′ t , y′ t ) and the equation of the line perpendicular to the asymptote is:

[0098]

[0099] make Substituting formula (15) into formula (14), we have:

[0100]

[0101] Solving equation (17) yields two solutions. Since the hyperbola takes the right branch, we take one of the positive values ​​as x′. A ; put x′ A Substitute the value of into formula (15) to obtain y′ A Similarly, by substituting equation (16) into equation (14), we can obtain t The coordinates of A and B when <0;

[0102] Let y′=y′ t Substituting into formula (14) we get:

[0103]

[0104] Solving equation (18) yields two solutions. Since the hyperbola takes the right branch, we take one of the positive values ​​as x′. B , y′ B =y′ t ;

[0105] After determining the search range, use the binary search method to quickly narrow the search range until ||AB|| is less than the threshold ε1; finally, r=min(||T′A||, ||T′B||);

[0106] Still taking the right branch of the standard hyperbola as an example, the process of binary search is as follows:

[0107] 1) y′=(y′ A +y′ B ) / 2 into formula (14) and we get:

[0108]

[0109] Select the positive root as x′ C The value of y′ C =(y′1+y′2) / 2, that is, the coordinate of the intersection point C of the straight line y′=(y′1+y′2) / 2 and the right branch of the standard hyperbola is (x′ C , y′ C );

[0110] 2) Compare ||T′A||, ||T′B|| and ||T′C||; if ||T′A|| is the largest, the search range is narrowed to between BC, and C is updated to A; if ||T′B|| is the largest, the search range is narrowed to between AC, and C is set to B;

[0111] 3) Calculate ||AB||. If ||AB|| is less than the threshold ε1, terminate the loop, r = min(||T′A||, ||T′B||), otherwise continue;

[0112] 4) Repeat steps (1) to (3);

[0113] Similarly, the same method can be used to determine the shortest distance r between the candidate position and the left branch of the standard hyperbola;

[0114] ② For special circumstances, that is or or

[0115] when The hyperbola becomes the equation of a straight line: x′=0, such as Figure 5 The diagram is a schematic diagram of solving r in a special case of the embodiment of the present invention, where r = x′ t ;

[0116] when When the hyperbola changes to S′ j is the ray with endpoints, if x′ t ≥x′ j , then r = y′ t ; otherwise, r=||T′S j ||;

[0117] when When the hyperbola changes to S′ i is the ray with endpoints, if x′ t ≤x′ i , then r = y′ t ; otherwise, r=||T′S i ||;

[0118] Finally, the weight α i，j Calculate according to the following formula (20):

[0119] α i，j =1 / r 2 (20).

[0120] Step 5: Substitute the weight calculated in step 4 into the constructed objective function to calculate the objective function values ​​corresponding to all candidate positions;

[0121] The objective function is the weighted square sum of the deviations between the measured value and the true value, and the objective function F(x, y) is expressed as:

[0122]

[0123] Among them, C N 2It means to select any two base stations from N base stations, which is the representation form of the combination formula; RDOA i，j The unknown position of the target and the base station S i and S j The distance difference is the measured value of the distance difference between the target and the two base stations; α i，j is the weight;

[0124] The objective function values ​​corresponding to all candidate positions can be obtained by formula (11).

[0125] Step 6: Find the minimum value from the objective function values ​​corresponding to all the candidate positions calculated. The candidate position corresponding to the minimum value is the final target estimated position.

[0126] In this step, a position is found to minimize the value of the objective function (11), that is, the weighted sum of squares of the errors is minimized. Then the candidate position corresponding to the minimum value is the final target estimated position, denoted as P f .

[0127] It is worth noting that the contents not described in detail in the embodiments of the present invention belong to the prior art known to professional and technical personnel in the field.

[0128] In summary, the method described in the embodiment of the present invention has the following advantages:

[0129] 1. Compared with the common weighted least square (WLS) algorithm, this method does not have the problem of ignoring the higher-order terms of noise, so it is more robust and can still be solved when the base stations are on the same straight line;

[0130] 2. Compared with traditional nonlinear optimization methods, this method avoids the selection of initial values ​​and prevents falling into local optimal solutions. More importantly, this method not only considers the influence of measurement errors, but also the influence of geometric conditions on position estimation, while traditional methods often ignore this important factor of geometric conditions;

[0131] 3. Compared with the geometric method, this method makes full use of redundant information and improves the accuracy of position estimation;

[0132] 4. Under the condition of measurement redundancy, this method can reflect whether there are abnormal measurement values ​​among many measurements, that is, observations with extremely large errors, and has the ability to shield abnormal measurements to achieve more robust position estimation, which is unmatched by any other TDoA-based positioning method.

[0133] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims. The information disclosed in the background technology section of this article is only intended to deepen the understanding of the overall background technology of the present invention, and should not be regarded as an admission or in any form that the information constitutes prior art known to those skilled in the art.

Claims

1. A search weighted positioning method based on TDoA, characterized in that: The method comprises: Step 1: When the number of base stations is equal to 3, an analytical solution is directly obtained by establishing an equation, and the analytical solution is the final target estimated position; The process of step 1 is specifically as follows: Assume that the coordinates of the i-th base station are S i (x i ,y i ,h i ), where h i is the vertical height difference between base station i and the target, i = 1, 2, ..., N, N is the total number of base stations, and the actual position of the target at the kth moment is P k (x k ,y k ), and its estimate is To achieve TDoA-based positioning, at least three base stations are required, that is, N ≥ 3. The known TDoA measurement can be converted into a distance-related measurement, as shown in formula (1): Where c is the speed of sound in m / s. Base station 1 is used as the reference point, and the target and base station S i The difference between the distance between the base station and the reference base station; When N = 3, use the measurement Instead of real RDOA i1，k , the solution obtained Yes P k The specific solution process is as follows: Subtract ① from ② and ③ in formula (2) to get: in is the distance between the target and base station 1; x 12 =x1-x2,y 12 =y1-y2,x 13 =x1-x3,y 13 =y1-y3, as well as The solution of formula (3) can be divided into two cases: The three base stations are not on the same straight line, that is, x 12 y 13 ≠x 13 y 12 ; The three base stations are on the same straight line, that is, x 12 y 13 =x 13 y 12 ;In both cases, the three base stations are at different locations; When x 12 y 13 ≠x 13 y 12 When , we can get from formula (3) and The relationship is shown in formula (4): in, Substituting equation (4) into equation (2) yields a The quadratic equation of one variable is as follows: in, Obviously, equation (6) has two solutions, but only one of them can be selected as Solution, let Δ = b 2 -4ac, select The guidelines are as follows: ① If Δ ≥ 0, equation (6) has two real roots, namely (-b + √Δ) / (2a) and (-b - √Δ) / (2a), If both roots are positive, the smaller one is chosen as Otherwise, choose the larger one; ② If Δ<0, equation (6) has two complex roots, then take its real part as The solution is Bundle Substituting into equation (4) we can get the estimated position of the target When x 12 y 13 =x 13 y 12 When , equation (4) is not valid because the denominators in equation (5) are all zero. Therefore, equation (3) needs to be solved by the following method, which can be divided into three cases: 1) If x 12 =0, there must be y 12 ≠0, otherwise base station 1 and base station 2 are at the same location, so x 13 =0 and y 13 ≠0, multiply both sides of equation (3) by y 13 , and multiply both sides of equation ② by y 12 ,So It can be solved by formula (8): 2) If y 12 =0, same as situation ①, there must be x 12 ≠0, then x 13 ≠0 and y 13 =0, at this time Solve through formula (9): 3) If x 12 ≠0 and y 12 ≠0, then It can be solved by equation (8) or (9); In seeking Then, substitute it into equations ① and ② in equation (2) to obtain the estimated position of the target. Step 2: When the number of base stations is greater than 3, calculate the number of combinations of three base stations, and solve the analytical solution of the target location based on TDoA for each combination; Step 3: Based on the analytical solution of the target position obtained in step 2, a rectangular search area is constructed; In step 3, the process of constructing a rectangular search area is as follows: Using the minimum value of the horizontal coordinate of all three base station combination solutions and maximum value And the minimum value of the vertical axis and maximum value Construct the vertex coordinates of the rectangular search area: and Step 4: Then select candidate positions in the constructed rectangular search area, and calculate the weights of the corresponding candidate positions for all candidate positions; In step 4, the process of selecting candidate positions in the constructed rectangular search area is as follows: Use m horizontal lines and n vertical lines to equally divide the rectangular search area. The intersection points of the horizontal lines and vertical lines, the intersection points of the horizontal lines and the sides of the rectangle, the intersection points of the vertical lines and the sides of the rectangle, and the vertices of the rectangle constitute all candidate positions, totaling (m+2)·(n+2); The weight calculation process corresponding to the candidate position is: First, the noise is measured at the distance difference between the candidate location and the two base stations to obtain After the rotation and translation of the coordinate system, for the general case, the coordinates of the two base stations and Constructing a single standard hyperbola, and solving the shortest distance r from the candidate position to the single standard hyperbola; For special cases, the coordinates of the two base stations and Construct a straight line or ray, and calculate the shortest distance r from the candidate position to the straight line or ray; The weight α i，j Calculate according to the following formula: α i，j ＝1 / r 2 ； Step 5: Substitute the weight calculated in step 4 into the constructed objective function to calculate the objective function values ​​corresponding to all candidate positions; wherein the objective function is the weighted square sum of the deviations between the measured value and the true value; Step 6: Find the minimum value from the objective function values ​​corresponding to all the candidate positions calculated. The candidate position corresponding to the minimum value is the final target estimated position.

2. The TDoA-based search weighted positioning method according to claim 1, characterized in that: In step 2, when the number of base stations is greater than 3, that is, N>3, for N base stations, there are M 3-base station combinations, and the value of M is determined by the following formula, where 'C' represents the combination operator and '! ' represents the factorial operator: For M combinations of three base stations, each base station combination uses the solution method when N=3 in step 1 to find an analytical solution for the target estimated position, a total of M, forming a set S.

3. The TDoA-based search weighted positioning method according to claim 1, characterized in that: The weight α i，j The specific calculation process is: Choose two different base stations S i and S j , whose coordinates are S i (x i ,y i ), S j (x j ,y j ); Select a candidate position with coordinates T(x t ,y t ), then the unknown position of the target and the base station S i and S j The distance difference RDOA i，j The value of can be calculated by formula (12): Set the current measurement noise to Δd i，j ,make Assume there is a position point Q that satisfies where ||QS i || represents point Q and base station S i distance; In general, when When , point Q is on a hyperbola; In special cases, when When Q is on a straight line, When , point Q is on the ray; ① For general situations, that is In order to calculate the weights conveniently, the coordinate system needs to be transformed first, that is, rotation and translation operations are performed so that after the coordinate system transformation, the base station S i and S j They are on the x-axis, and their centers are at the origin. The method of rotating and translating the coordinate system is shown in formula (13): in: After the coordinate system is transformed, A single standard hyperbola is constructed for the distance difference. After the rotation and translation of the coordinate system, the equation of the constructed single standard hyperbola is as follows: in: like Then take the left branch of a single standard hyperbola (14); if Then take the right branch of a single standard hyperbola (14); Assume that the candidate position T(x t ,y t ) after rotation and translation according to formula (13) is T′(x′ t , y′ t ), with T′(x′ t , y′ t ) as the center, when the circle is tangent to a single branch of the single standard hyperbola (14), the radius r is the shortest distance from the position of the point to be determined to the hyperbola; Assuming the coordinates of the tangent point are P′0(x′0, y′0), then r = ||T′ P′0||. However, P′0(x′0, y′0) is not easy to solve directly, so we search for a point P′0(x′0, y′0) on a single standard hyperbola that satisfies [(x′ t -x′0) 2 +(y′ t -y′0) 2 ]minimum; In order to speed up the numerical solution, the search range is limited to between points A and B on a single standard hyperbola, where point A(x′ A , y′ A ) is a point through T′(x′ t , y′ t ), and the intersection of the straight line perpendicular to the asymptote and the single standard hyperbola; point B(x′ B , y′ B ) is the straight line y′=y′ t Intersection point with a single standard hyperbola; The following takes the right branch of the standard hyperbola as an example to introduce the process of determining the coordinates of points A and B: When y′ t ≥0, through point T′(x′ t , y′ t ) and the equation of the line perpendicular to the asymptote is: When y′ t <0, passing through point T′(x′ t , y′ t ) and the equation of the line perpendicular to the asymptote is: make Substituting formula (15) into formula (14), we have: Solving equation (17) yields two solutions. Since the hyperbola takes the right branch, we take one of the positive values ​​as x′. A ; put x′ A Substitute the value of into formula (15) to obtain y′ A Similarly, by substituting equation (16) into equation (14), we can obtain t The coordinates of A and B when <0; Let y′=y′ t Substituting into formula (14) we get: b 2 x′ 2 -a 2 y′ t 2 -a 2 b 2 =0 (18) Solving equation (18) yields two solutions. Since the hyperbola takes the right branch, we take one of the positive values ​​as x′. B , y′ B =y′ t ; After determining the search range, use the binary search method to quickly narrow the search range until ||AB|| is less than the threshold ε1; finally, r=min(||T′A||, ||T′B||); Still taking the right branch of the standard hyperbola as an example, the process of binary search is as follows: 1) Set y′=(y′ A +y′ B ) / 2 into formula (14) and we get: 4b 2 x′ 2 -a 2 (y′1+y′2) 2 -4a 2 b 2 =0 (19) Select the positive root as x′ C The value of y′ C =(y′1+y′2) / 2, that is, the coordinate of the intersection point C of the straight line y′=(y′1+y′2)2 and the right branch of the standard hyperbola is (x′ C , y′ C ); 2) Compare ||T′A||, ||T′B|| and ||T′C||; if ||T′A|| is the largest, the search range is narrowed to between BC, and C is updated to A; if ||T′B|| is the largest, the search range is narrowed to between AC, and C is set to B; 3) Calculate ||AB||. If ||AB|| is less than the threshold ε1, terminate the loop, r = min(||T′A||, ||T′B||), otherwise continue; 4) Repeat steps (1) to (3); Similarly, the same method can be used to determine the shortest distance r between the candidate position and the left branch of the standard hyperbola; ② For special circumstances, that is or or when The hyperbola becomes a straight line equation: x′=0, at this time r=x′ t ; when When the hyperbola changes to S′ j is the ray with endpoints, if x′ t ≥x′ j , then r = y′ t ; otherwise, r=||T′S j ||; when When the hyperbola changes to S′ i is the ray with endpoints, if x′ t ≤x′ i , then r = y′ t ; otherwise, r=||T′S i ||; Finally, the weight α i，j Calculate according to the following formula (20): α i，j ＝1 / r 2 (20)。 4. The TDoA-based search weighted positioning method according to claim 1, characterized in that: In step 5, the objective function F(x, y) is expressed as: Among them, C N 2 It means to select any two from N base stations, which is the representation form of the combination formula; RDOA i，j The unknown position of the target and the base station S i and S j The distance difference; is the measured value of the distance difference between the target and the two base stations; α i，j is the weight; The objective function values ​​corresponding to all candidate positions can be obtained by formula (11).

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